1972 국제수학올림피아드 4번문제

다음 연립부등식의 모든 양의 실수해 $(x_1,x_2,x_3,x_4,x_5)$를 구하여라. \begin{align*} (x_1^2-x_3x_5)(x_2^2-x_3x_5) &\leq 0 \\ (x_2^2-x_4x_1)(x_3^2-x_4x_1) &\leq 0 \\ (x_3^2-x_5x_2)(x_4^2-x_5x_2) &\leq 0 \\ (x_4^2-x_1x_3)(x_5^2-x_1x_3) &\leq 0 \\ (x_5^2-x_2x_4)(x_1^2-x_2x_4) &\leq 0 \end{align*}

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